i$f> Theory of Cryjlallifation. 



theory has arrived at the utmoft point of accuracy. What I 

 here fay takes place alfo in regard to all the other refults of 

 theory compared with thofe of calculation ; and it is obvious 

 that if this theory were falfe, it would conduct to errors 

 which the instrument would not fail to render fenfible, by 

 the orcat differences which it would give between the angles 

 found by calculation and thofe found by meafurement. 



M. Vemer and M. Rome de l'Me have confounded the 

 dodecaedron of pvrites with the regular dodecaedron of geo- 

 metry, in which each pentagon has all iis fides equal, and all 

 its ancles equal alfo* . If thefe two celebrated mineralogifts 

 had made more tife of gtometrv in confidering cryftals, they 

 would have perceived a very (biking difference between thefe 

 two dodecaedra, finee tke regular dodecaedron gives only 

 n6' 33 '54 / as the inclination of its refpe&ive pentagons, 

 which makes a difference of about n° \ between it and that 

 above mentioned. Nav, there is no law of decrement what- 

 ever capable of producing the regular dodecaedron, however 

 compound it may be imagined, as I have {hewn eliewhere f 

 in regard to a cubic nucleus, and as I can demonstrate at 

 prefent, generally, for a nucleus of any form. Alter thefe 

 details il may be eafily feen how important the ufe of cal- 

 culation is, cither to prove the truth of theory, or to trace 

 out the boundaries by which the progrefs of crvftallifation is 

 circumfcribcd. 



We have already then two kinds of dodecaedra ; one, 

 whole faces are rhombufes ; and another, whole faces arc 

 pentagons: produced upon a cubical nucleus, in confequence 

 of two fimple and regular laws of decrement, in a dire&ion 

 parallel to the edges of the nucleus, A multitude of new 

 .Ira, which will have the fame nucleus, may be con-, 

 ftrucled, by varving thefe laws in divers other ways. 



■ 7a; '.-.:' ■■/. ■€■■>:■■■ ' 'la, page i S4. See alio, La Crjflallograpble 



* M de !'!_:!■■. r. iii. p. 132 anil 133, 

 + Mem-d f Ac-ad. cfet Sciences, ann i-c 1785, p. 3*3. 



Qalc#requ$ 



